50% buff vs Attack Speed +1 for Explorer mages post Destiny
Typed this up in a thread reply but no idea why reddit keeps screwing up formatting, so here I go...
I just came back from some number crunching + discussions with several adventurer mage players. I'm from MSEA, so I'll using MSEA naming here, but I'll append GMS naming as best as my memory serves me. The tests were done in MSEA context as well, so please bear in mind we don't have familiars etc, only MPE Green potion which allows us to break the soft cap (2).
It turns out that people are quite mistaken about the importance of AS+1 because of the initial eyeballing of the deal cycle from the KMS chart maker. Raw info here for each of the mages:
So it appears of all the mages, Bishops at first glance seem to be the one most in need of AS+1, because our Angel Ray alone takes up 40% of the deal ratio, and Angel Ray is directly affected be attack speed. And as of pre-Destiny, Prayer (Benediction) does not affect cast speed of Angel Ray.
Or is it?
As a Bishop main, I'll be focusing on Bishop values, but as the other mages have a bigger deal ratio belonging to skills that are NOT attack speed dependent, I would think that they will tend to trend more heavily towards 50% Buff Duration.
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For one, do note that 60% (or even more in combat situations) of a Bishop's deal ratio is non-attack speed dependent, and our main burst skill is Divine Punishment, pretty much a stand-and-manfight skill.
If we're comparing the merits of 50% buff vs +1 atkspd, we have to find something in common to compare possible damage loss against: the 38% buff duration 2nd IA line which mages have to roll for players who roll a first-line +1 atkspd.
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Some important values to take note before delving into the calculations, values are taken from my own Bishop:
Infinity additive 3% FinalDmg tick interval: 5s. Infinity's 3% final damage boost is confirmed to stack additively. This was the most stable interval, I have had 6s and 7s intervals from MSEA's shitty world class servers.
Buff Duration on stat window: 180%
Relevant buffs: Decent Combat Orders (this will probably be a realistic staple in combat situations), Decent Speed Infusion (atkspd +1, also another realistic staple buff in combat)
Main relevant IA line: 50% buff duration
Angel Ray Speed(0) cast time: 0.51s
Angel Ray Speed(1) cast time: 0.57s
Infinity's initial final damage boost upon cast = 71% due to DCO.
Infinity's base duration = 41s due to DCO.
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Therefore,
Infinity duration with 50% buff = 41 x (1 + 180/100) = 114.8s
Infinity duration with 38% buff = 41 x (1 + 168/100) = 109.88s
Given the steady 3% FD increase every 5s, along with the initial 71% FD upon cast, we can plot a linear graph in the form of y = 0.6x + 71 of FD% vs Time in seconds, to see what how much damage is missing from 38% buff vs 50% buff via area under line. It should be a trapezium.
So damage dealt difference (or loss) is 0.5 x (a+b) x h, where a denotes the %FD reached where Infinity ends at 109.88s from the 38% buff, and b denotes the %FD reached where Infinity ends at 114.8s from the 50% buff. h is simply the x-axis distance between these 2 points.
Thus damage difference = 0.5 x (136.928 + 139.88) x (114.8 - 109.88) = 680.94768 FD% seconds. This is the amount of accumulated damage that AS0 has to beat, in nearly 5 seconds.
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For another comparison, let’s look at the first 109 seconds between the two with Angel Ray casts, for it is Infinity’s duration with 38% buff.
With +1 atkspd, or AS(0), there will be a total of 213 Angel Rays fired.
With 50% buff, or AS(1), there will be a total of 191 Angel Rays. The final 5 seconds can then be spent with a Divine Punishment finisher.
Alternatively, if we are to include full 8s Divine Punishment keydowns at the end,
With +1 atkspd, we will get 199 Angel Rays.
With 50% buff, we will get 185 Angel Rays and a harder hitting Divine punishment.
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Another element in this discussion that we have to examine is the flaws in how the deal ratio was obtained. Take for example, the graph of Bishop’s cumulative damage deal over time, at Attack speed 2 (the soft cap of KMS).
At t= 105s, the curve starts spiking steeply. The only possible skill that can do this in a Bishop’s arsenal is Divine Punishment. We know that the DPM guy designed this with 50% buff/10% boss/8% debuff in mind, as seen in this line in the script: SpecLegendryAbility[rownames(SpecLegendryAbility)=="Bishop", ] <- c("BuffDuration", "BDR", "DisorderBDR")
F/p and i/L Inner Abilities were designed with 50% buff/20% Crit Rate/8% debuff damage in mind as well:
SpecLegendryAbility[rownames(SpecLegendryAbility)=="ArchMageFP", ] <- c("BuffDuration", "CRR", "DisorderBDR")
SpecLegendryAbility[rownames(SpecLegendryAbility)=="ArchMageTC", ] <- c("BuffDuration", "CRR", "DisorderBDR")
The timing fits perfectly into the 114.8s infinity setup as well. It also meant that the DPM chart maker only casted Divine Punishment once during one cycle of Infinity.
However, in actual combat, like punch king or Sewers, you would cast a volley of Divine Punishment either at the start or at the 20-30s mark, as the 8s of Holy light charges will be replenished by the time you reach the tail end of the Infinity buff; it takes 68s for full replenishment.
This optimization alone would probably nearly double Divine Punishment’s deal ratio (initially 20% in the original DPM chart) without other external factors.
Also, in bossing/sewers/dojo situations, there are significant external buffs that are bundled with Divine Punishment, and will further boost Divine Punishment’s weight in the deal ratio as well. This are most popularly buffs like: Weapon Jump, Ring of Restraint, Angelic buster’s link skill Terms and Conditions, and others which I can’t remember off the top of my head.
A cherry on top would perhaps be the fact that AB’s link skill is affected by buff duration and skill cooldown.
Finally, in taking +1 attack speed and 38% buff, you can only take in 10% boss, 8% debuff, or 20% critical rate. 50% buff duration takes in 2 of those, and crit rate isn’t needed for Bishops.
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To conclude,
TL;DR: 50% maybe wins +1 atkspd/38% buff? I would expect this result to be similar with the other 2 mages, as their attack speed dependent deal ratios are smaller than Angel Ray. YMMV.
DPM chart assumes that we have 0 cast time for all our burst buff. Realistically that won’t be the case, and we will definitely lose those precious seconds in buffing up for a burst.
Also 50% buff would be better for training if you’re trying to 1-2hit mobs stably. This is especially so in Grandis areas with Authentic/Sacred Force.
Or I could be completely wrong with my math and ideas. But what do I know, I eat crayons.
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Edit: My crayon math was off. Need to find other stationeries...
Excluding the effect of 8% debuff, AS+1 wins 50% buff by an average of 4% damage without considering other external effects that do not benefit from AS+1. This includes things like auto attacks from Angel of Libra, Triumph Feather, Holy Fountain etc:
1 Infinity unoptimised:
library(tidyverse)
AR_1_hit<-3910037344
Divine_8s<-65668920940
end_infinity_109s <- (131+134)/2
end_infinity_114s <- (134+137)/2
num_casts_5s <-ceiling(5/0.51)
ramp_infinity_109s <- seq(from=71, to=131, by=3)%>%mean()
ramp_infinity_114s <- seq(from=71, to=134, by=3)%>%mean()
AS_0 <- (end_infinity_109s*Divine_8s) + (ramp_infinity_109s*AR_1_hit*ceiling(101/0.51)) + (AR_1_hit*num_casts_5s)
AS_1 <- (end_infinity_114s*Divine_8s) + (ramp_infinity_114s*AR_1_hit*ceiling(106/0.57))
AS_0/AS_1
Difference = 4.6%
1 infinity optimised:
AR_1_hit<-3910037344
Divine_8s<-65668920940
mid_infinity_109s <- (83+86)/2 #fd% average for first DP
mid_infinity_114s <- (86+89)/2
end_infinity_109s <- (131+134)/2 #fd% for last DP
end_infinity_114s <- (134+137)/2
num_casts_5s <-ceiling(5/0.51)
ramp_infinity_109s_start <- seq(from=71, to=83, by=3)%>%mean() #4 ticks, t=0 to t=25
ramp_infinity_114s_start <- seq(from=71, to=86, by=3)%>%mean() #5 ticks, t=0 to t=30
ramp_infinity_109s_end <- seq(from=89, to=131, by=3)%>%mean() #t=33 to t=101
ramp_infinity_114s_end <- seq(from=92, to=134, by=3)%>%mean() #t=38 to t=106
AS_0 <- (ramp_infinity_109s_start*AR_1_hit*ceiling(25/0.51)) + (mid_infinity_109s*Divine_8s) +
(ramp_infinity_109s_end*AR_1_hit*ceiling(68/0.51)) + (end_infinity_109s*Divine_8s) + (AR_1_hit*num_casts_5s)
AS_1<- (ramp_infinity_114s_start*AR_1_hit*ceiling(30/0.57)) + (mid_infinity_114s*Divine_8s) +
(ramp_infinity_114s_end*AR_1_hit*ceiling(68/0.57)) + ((end_infinity_114s*Divine_8s))
AS_0/AS_1
Difference = 3.6%
2 back-to-back infinities, unoptimised:
AR_1_hit<-3910037344
Divine_8s<-65668920940
mid_infinity_109s <- (83+86)/2 #fd% average for first DP
mid_infinity_114s <- (86+89)/2
end_infinity_109s <- (131+134)/2 #fd% for last DP
end_infinity_114s <- (134+137)/2
num_casts_10s <-ceiling(10/0.51)
ramp_infinity_109s <- seq(from=71, to=131, by=3)%>%mean()
ramp_infinity_114s <- seq(from=71, to=134, by=3)%>%mean()
ramp_infinity_109s_start <- seq(from=71, to=83, by=3)%>%mean() #4 ticks, t=0 to t=25
ramp_infinity_114s_start <- seq(from=71, to=86, by=3)%>%mean() #5 ticks, t=0 to t=30
ramp_infinity_109s_end <- seq(from=89, to=131, by=3)%>%mean() #t=33 to t=101
ramp_infinity_114s_end <- seq(from=92, to=134, by=3)%>%mean() #t=38 to t=106
AS_0 <- (ramp_infinity_109s_start*AR_1_hit*ceiling(25/0.51)) + (mid_infinity_109s*Divine_8s) +
(ramp_infinity_109s_end*AR_1_hit*ceiling(68/0.51)) + (end_infinity_109s*Divine_8s) +
(end_infinity_109s*Divine_8s) + (ramp_infinity_109s*AR_1_hit*ceiling(101/0.51)) + (AR_1_hit*num_casts_10s)
AS_1<- (ramp_infinity_114s_start*AR_1_hit*ceiling(30/0.57)) + (mid_infinity_114s*Divine_8s) +
(ramp_infinity_114s_end*AR_1_hit*ceiling(68/0.57)) + ((end_infinity_114s*Divine_8s)) +
(end_infinity_114s*Divine_8s) + (ramp_infinity_114s*AR_1_hit*ceiling(106/0.57))
AS_0/AS_1
Difference = 4.14%
2 back-to-back Infinites, optimised:
AR_1_hit<-3910037344
Divine_8s<-65668920940
mid_infinity_109s <- (83+86)/2 #fd% average for first DP
mid_infinity_114s <- (86+89)/2
mid_infinity_109s_a <- (110+113+116)/3
mid_infinity_114s_a <- (110+113+116)/3
end_infinity_109s <- (131+134)/2 #fd% for last DP
end_infinity_114s <- (134+137)/2
num_casts_10s <-ceiling(10/0.51)
ramp_infinity_109s_start <- seq(from=71, to=83, by=3)%>%mean() #4 ticks, t=0 to t=25
ramp_infinity_114s_start <- seq(from=71, to=86, by=3)%>%mean() #5 ticks, t=0 to t=30
ramp_infinity_109s_start_a <- seq(from=71, to=110, by=3)%>%mean() #from t=0 to t=68
ramp_infinity_114s_start_a <- seq(from=71, to=110, by=3)%>%mean()
ramp_infinity_109s_end <- seq(from=89, to=131, by=3)%>%mean() #t=33 to t=101
ramp_infinity_114s_end <- seq(from=92, to=134, by=3)%>%mean() #t=38 to t=106
ramp_infinity_109s_end_a <- seq(from=116, to=134, by=3)%>%mean() #t=76 to t=109
ramp_infinity_114s_end_a <- seq(from=116, to=137, by=3)%>%mean() #t=76 to t=114
AS_0 <- (ramp_infinity_109s_start*AR_1_hit*ceiling(25/0.51)) + (mid_infinity_109s*Divine_8s) +
(ramp_infinity_109s_end*AR_1_hit*ceiling(68/0.51)) + (end_infinity_109s*Divine_8s) +
(ramp_infinity_109s_start_a*AR_1_hit*ceiling(68/0.51)) + (mid_infinity_109s_a*Divine_8s) +
(ramp_infinity_109s_end_a*AR_1_hit*ceiling(33/0.51)) + (AR_1_hit*num_casts_10s)
AS_1<- (ramp_infinity_114s_start*AR_1_hit*ceiling(30/0.57)) + (mid_infinity_114s*Divine_8s) +
(ramp_infinity_114s_end*AR_1_hit*ceiling(68/0.57)) + (end_infinity_114s*Divine_8s) +
(ramp_infinity_114s_start_a*AR_1_hit*ceiling(68/0.57)) + (mid_infinity_114s_a*Divine_8s) +
(ramp_infinity_114s_end_a*AR_1_hit*ceiling(38/0.57))
AS_0/AS_1
Difference = 3.99%
So AS+1 beats 50% buff by 3.6% - 4.6% damage without considering other IA lines 50% buff has, in a scenario with 0 infinity downtime. So in Destiny when we're looking at 99% uptime for 50% buff vs 98% uptime for 38% buff for the revamped Unstable memory, I'd expect this difference to be smaller. Not included in this calculation is the constant damage ramping from Triumph Feather, and possibly Holy Fountain, which will further close out the difference.
As seen in the calculations, the difference tends towards 4% assuming 100% infinity uptime, in a naked Infinity-only setting.
Then again, since Bishops are mainly support in parties, let's run the code again with 0AS on 50% buff duration and look at the difference to see how much 50% buff wins by in a 0AS setting. This should still be very realistic considering every class tree has a job that gives at least +1AS party buff, and Kannas will still be everywhere.
1 Infinity, unoptimised: +5.64%
1 Infinity, optimised: +5.73%
2 Infinities, unoptimised: +5.68%
2 Infinities, optimised: +5.91%
These values are WITHOUT other damage-boosting buffs. Let's say if there is a buff that goes straight to the Final Damage% pool, say 11% from Kanna's Spirit Domain, then AS1, 50% buff beats out AS0. Also an AS1 Bishop also has 8% debuff damage over an AS0 Bishop:
AR_1_hit<-3910037344
Divine_8s<-65668920940
end_infinity_109s <- (131+134)/2
end_infinity_114s <- (134+137)/2
num_casts_5s <-floor(5/0.51)
ramp_infinity_109s <- seq(from=71, to=131, by=3)%>%mean()
ramp_infinity_114s <- seq(from=71, to=134, by=3)%>%mean()
AS_0 <- (end_infinity_109s*Divine_8s) + (ramp_infinity_109s*AR_1_hit*ceiling(101/0.57)) + (AR_1_hit*num_casts_5s)
AS_1 <- (end_infinity_114s*Divine_8s) + (ramp_infinity_114s*AR_1_hit*ceiling(106/0.57))
AS_1 <- 1.11*AS_1
AS_0/AS_1
Difference = +17.2%. Then again, I doubt that there is any lack of Kannas to pair up with AS1 and AS0 Bishops, but if that were the case, the AS1 bishop would be sitting at AS0 in a Domain setting anyway...
So is the difference still worth it to consider playing a solo Bishop on AS0? You're your best judge, but I guess I'll still stick to AS1 with 50% buff as a party Bishop in view of most endgame bosses leaning hard towards party play.
For mages with low deal ratios of attack speed dependent attacks... Here's your answer I guess. 40% attack speed-dependent deal for a 4% damage difference, so those with <20% deal cycles should see even less, or even 50% buff being outright stronger depending on your rotation
Edit 2: Tweaked code to account for Angel Rays already in the air upon cast
Posted May 7, 2022, 11:06 PM UTC · edited